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  • 1
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 39 (1993), S. 1007-1017 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model is developed that predicts three-dimensional, two-phaseflow, heat transfer and reaction inside catalytic cracking riser-type reactors. The model consists of the full set of partial-differential equations that describe the conservation of mass, momentum, energy and chemical species for both phases in the reactor, coupled with empirical correlations concerning interphase friction, interphase heat-transfer and fluid-to-wall frictional forces. The cracking reaction is simulated by a simple three-lump kinetic model, but more realistic kinetic models can be easily included. The model can predict the most important engineering aspects of a riser reactor including pressure drop, catalyst holdup, interphase slip velocity, catalyst acceleration zone, choking behavior and temperature distribution in both phases, and yields distribution all over the reactor. It can also predict other complex engineering three-dimensional, two-phase problems realistically using computational fluid dynamics techniques.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 39 (1993), S. 1799-1809 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Nonisothermal adsorption is studied by incorporating its mathematical description into a model consisting of the full two-dimensional Navier-Stokes equations and energy and species concentration equations to simulate the processes in fixed-bed industrial adsorbers/regenerators. The model partial-differential equations are solved numerically by using well-established computational fluid dynamics techniques. The equilibrium between gas and solid is considered nonlinear, which is described by Freundlich-type equations. The transport and adsorption of a compound from a solvent to and into an adsorbent are described by a two-step process: transport through the “film” to the outer surface of the particle and diffusion into the porous particle. The effect of fill resistance is discussed, as well as a two-equation turbulence model. Solutions obtained for a typical industrial adsorber/regenerator demonstrate the potential of this method. The computed results for various flow ratios and parameters in the Freundlich equations are shown to be physically plausible.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 103-112 
    ISSN: 0271-2091
    Keywords: Supersonic ; Subsonic ; Mach Disc ; Compressible Pressure-correction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An analytical model has been developed for computing embedded subsonic flow in rocket plumes from underexpanded axisymmetric supersonic nozzles. Numerical procedures based on the analysis have been incorporated in a simplified, non-reacting exhaust structure program and calculations for representative plume conditions performed. The technique is numerically stable and has provided satisfactory predictions of Mach-disc associated embedded subsonic flow.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 129-153 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A comparative study of eight discretization schemes for the equations describing convection-diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central, upwind and hybrid difference schemes,1,2 together with the quadratic upstream,3,4 quadratic upstream extended4 and quadratic upstream extended revised difference4 schemes. Also tested are the so called locally exact difference scheme5 and the power difference scheme.6 In multi-dimensional problems errors arise from ‘false diffusion’ and function approximations. It is asserted that false diffusion is essentially a multi-dimensional source of error. Hence errors associated with false diffusion may be investigated only via two- and three-dimensional problems. The above schemes have been tested for both one- and two-dimensional flows with sources, to distinguish between ‘discretization’ errors and ‘false diffusion’ errors.7 The one-dimensional study is reported in Reference 7. For 2D flows, the quadratic upstream difference schemes are shown to be superior in accuracy to the others at all Peclet numbers, for the test cases considered. The stability of the schemes and their CPU time requirements are also discussed.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 927-952 
    ISSN: 0271-2091
    Keywords: Turbulence ; Rapid Compression Expansion ; Bowl-in-piston ; TDC ; BDC ; Inclined Walls ; PHOENICS ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper presents two- and three-dimensional computations of the in-cylinder turbulent flow in a diesel engine. The mathematical formulation is presented first, with emphasis on the modifications made to the standard k-ε model of turbulence, to account for rapid compression/expansion, and on the k-w model also used in the computations. Then, the results of two-and three-dimensional transient calculations are presented and compared with experimental data. It is realized that two-dimensional computations may be of little value to real engines, which would probably require three-dimensional analyses. However, two-dimensional studies are still useful in allowing the testing of new ideas easily and economically. It is concluded that the standard k-ε model may lead to poor predictions when used for internal combustion (IC) engine simulations, and that the modified model leads to more reasonable length-scale distributions, and it improves significantly the overall agreement of velocity predictions with experiment. The effect of the k-ε modification is apparent in both the two- and three-dimensional simulations. It is also demonstrated that the k-w model provides better turbulence predictions than the unmodified k-ε model, for the cases considered, and that a similar modification of the k-w model, to account for rapid compression/expansion, might improve its predictions even further.
    Additional Material: 22 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 225-244 
    ISSN: 0271-2091
    Keywords: Convection-Diffusion ; Differencing Schemes ; Discretization Errors ; False Diffusion ; Upwind Scheme ; Higher Order Schemes ; Accuracy ; Stability ; Computational Cost ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A comparative study of seven discretization schemes for the equations describing convection-diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central- and upwind-difference schemes, together with the Leonard,1 Leonard upwind1 and Leonard super upwind difference1 schemes. Also tested are the so called locally exact difference scheme2 and the quadratic-upstream difference scheme.3,4 In multidimensional problems errors arise from ‘false-diffusion’ and function approximations. It is asserted that false diffusion is essentially a multidimensional source of error. No mesh constraints are associated with errors in function approximation and discretization. Hence errors associated with discretization only may be investigated via one-dimensional problems. Thus, although the above schemes have been tested for one- and two-dimensional flows with sources, only the former are presented here. For 1D flows, the Leonard super upwind difference scheme and the locally exact scheme are shown to be far superior in accuracy to the others at all Peclet numbers and for most source distributions, for the test cases considered. Furthermore, the latter is shown to be considerably cheaper in computational terms than the former. The stability of the schemes and their CPU time requirements are also discussed.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 263-276 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computer model has been developed to study thermal energy releases into the environment. A typical application of the model is the study of the behaviour of cooling-tower effluent under different weather and operating conditions. The model employs the full three-dimensional transport equations describing the conservation of mass, momentum and energy. The flow is treated as single-phase and the behaviour of any droplets present is calculated indirectly. The model takes into account such hydrometeorological phenomena as the effects of humidity, wind direction and speed, density variations and the presence and precipitation of droplets. Sample results from cooling tower applications are presented and discussed.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 643-657 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The moving boundary (i.e. the piston) within a reciprocating engine poses the problem that as it moves towards the cylinder head it compresses the computational grid lines. Control cells that started with reasonable aspect ratios become so compressed that aspect ratios of 1000 are not unusual in some cases. This, of course, adversely affects numerical accuracy and convergence. It is the purpose of this paper to present a conservative scheme that allows for the removal and addition of grid cells, during simulation, so as to restore reasonable aspect ratios. Results of the computations are presented and compared with experimental data. It is concluded that with the proposed scheme convergence is obtained within fewer iterations, CPU time is reduced and the results are generally in better agreement with experimental data.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 2607-2615 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model has been developed that predicts the effects of design parameters, operating variables and physical properties on the performance of a membrane reactor with a permeselective wall. The model consists of the full set of partial differential equations that describe the conservation of mass, momentum and chemical species, coupled with chemical kinetics and appropriate boundary conditions for the physical problem. The solution of this system is obtained by a finite-volume technique. The model was applied to study the dehydrogenation of cyclohexane. Two membrane types in tubular form were studied: a selective porous glass with low gas permeabilities and a porous alumina with very high gas permeabilities. It is concluded that gas separation and reactor performance are strongly influenced by dispersion effects only in the latter membrane reactor, while in both cases radial concentration profiles do not correspond to those obtained with plug flow. Therefore, simulations of this type of problem should be based on complex dispersion models rather than the existing ideal plug-flow ones.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2279-2304 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An important limiting factor in the accurate modelling of fluid flow problems is the numerical representation of the convection terms in the Navier-Stokes equations. This paper reviews several approaches used to approximate the convection terms and reduce the so-called false-diffusion errors, within the context of finite-difference and finite-volume methods. Numerical errors are characterized as those due to discretization of the differential terms and those due to the influence of the multidimensional nature of the flow. Necessary criteria are identified which a numerical scheme must satisfy, if it is to be a candidate, at least in terms of accuracy and practicality, for the successful solution of the Navier-Stokes equations. One of the criteria is the need of the scheme to account explicitly for the multidimensionality of the flow in the transport of scalar variables. All schemes except Raithby's SKEW approximation are deficient in this respect. However, the SKEW scheme does not satisfy some of the other criteria and does not always perform well. A new scheme called CUPID (Corner UPwInDing), which is based on the ideas of the SKEW scheme, yet obeys more of the criteria identified above, is described. The scheme is tested on a series of discriminating test problems which, the authors contend, demonstrate its potential for practical use in solving accurately the Navier-Stokes equations.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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